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15.Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution.What must be true of a linear system for it to have a unique solution? Select all that apply.A.The system has no free variables.B.The system is inconsistent.C.The system has one more equation than free variable.D.The system is consistent.E.The system has at least one free variable.F.The system has exactly one free variable.Use the given assumption that the coefficient matrix of the linear system of four equations in four variables has a pivot in each column to determine the dimensions of the coefficient matrix.The coefficient matrix has rows and columns.fourfourLet the coefficient matrix be in reduced echelon form with a pivot in each column, since each matrix is equivalent to one and only one reduced echelon matrix. Construct a matrix with the dimensions determined in the previous step that is in reduced echelon form and has a pivot in each column.1000010000100001Now find an augmented matrix in reduced echelon form that represents a linear system of four equations in four variables for which the corresponding coefficient matrix has a pivot in each column. Choose the correct answer below.A.100a010b001c000dB.1000010000100001C.1000a0100b0010c0001dD.a00010b00100c01000d1Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by the augmented matrix consistent? Write the system of equations corresponding to the augmented matrix found above to determine the number of free variables.x1=ax2=bx3=cx4=dFree variables are variables that can take on any value. How many free variables are in the system?
7/12/2018Assignment 2 (1.2)-AMMAR ALSAIDI13/13x2x3x4x44x1Why does the system have a unique solution?